geometric-deep-learning

This paper introduces Latent Lie-Poisson Neural Networks (LLPNNs), a structure-preserving framework for learning Lie-Poisson dynamics directly from observable data, using geometric methods and Magnus-based Lie-group updates. It demonstrates strong accuracy and robustness on rigid body, underwater vehicle, and optimal control examples.

TAGTorch is an open-source PyTorch library that unifies tools for topology, algebra, and geometry-aware machine learning, covering preprocessing, architectures, training techniques, and model analysis.

This review surveys geometric deep learning (GDL) approaches for polypharmacology and multi-target drug design, covering architectures from graph neural networks to SE(3)-equivariant diffusion models for capturing 3D molecular structures.

Proposes HDE-Net, a manifold-constrained deep neural network that uses hyperbolic space to better model rule-based structures in tabular data, achieving state-of-the-art performance on the TALENT-tiny-core benchmark while maintaining efficiency.

This paper introduces the Large Cancer Assistant (LCA), a model-agnostic orchestration framework for scalable clinical decision support in oncology that decouples multimodal data ingestion from AI inference using a 7-tuple architecture and Algorithmic Impermeability.

A set of lecture notes covering the mathematics of neural networks, from basic activation functions to geometric concepts like group convolutions and equivariance.

This paper empirically measures the symmetry–data exchange rate predicted by equivariance theory, finding that wrong-group symmetry constraints are actively harmful, augmentation with test-time orbit averaging matches equivariant architectures, and the theoretical |G|-fold sample complexity reduction is only weakly confirmed with wide confidence intervals. The study is explicitly exploratory and not pre-registered.

This paper introduces coherence, a geometric constraint for neural representations inspired by grid cells and head direction cells in the brain. Coherence ensures that features respond to geometrically connected regions of the data manifold, improving interpretability; the authors propose a differentiable objective (Coh) and validate it on synthetic data, rotated MNIST, and BERT token embeddings.

Introduces Geometry-Aware Tabular Diffusion (GATD), which augments tabular diffusion denoisers with explicit pairwise geometric features. Achieves state-of-the-art performance on ten benchmarks while using significantly fewer parameters.

Presents EAMS, a lightweight equivariant mesh segmentation framework that generalizes across anatomical tasks, showing a trade-off between equivariance and accuracy on subtle features.

This paper analyzes oversmoothing in Neural Sheaf Diffusion (NSD) as a representation degeneracy phenomenon using quiver theory and Geometric Invariant Theory. It proposes moment-map-inspired regularizers and explores non-uniform stalk dimensions to mitigate this issue in heterophilic graph benchmarks.

This paper introduces CORE, a new knowledge graph completion model that uses cyclic orthotope relation embeddings on a torus manifold to address boundary constraints in region-based models. Experiments show competitive performance in link prediction tasks.

This paper presents a theoretical framework interpreting Transformer components (attention, residual connections, normalization) as arising from a spherical state estimation problem using Radial-Tangential SDEs.

This paper introduces Geometric Kolmogorov-Arnold Networks (GeoKAN), a family of geometry-aware models that learn Riemannian metrics to adapt coordinates for improved function approximation and physics-informed learning.

The paper introduces the EΔ-MHC-Geo Transformer, a novel architecture using adaptive geodesic operations with guaranteed orthogonality via Cayley rotations and Householder reflections. It demonstrates improved long-horizon stability and norm preservation compared to existing baselines like Deep Delta Learning.

This paper proposes AnisoAlign, a framework that addresses the modality gap in multimodal models by applying anisotropic geometric correction to enable effective unpaired modality alignment.